Removing Latex Paint From Cupboards

We recently bought a house where the wood cabinets had been painted white. What we didn't notice until we lived here is that they had been painted twice. The first coat was done properly, oil over primer.

The second is latex. No sanding. No priming. We've been here three weeks and it is peeling like crazy. I have gotten estimates ranging from $2,200 to "lady, just replace the cabinets, it would be cheaper". The paint expert at our local hardware store suggested I just peel the latex off, sand and prime, which is the cheapest option, but boring. Any advice?